Recently I finished chapter 14 in the book Art of Reasoning. The book is about how to think effectively and how to improve your thinking skills. I will give you a basic outline of what the book is about in its first 14 chapters.
What is logic?
What if you’re able to take information that you’ve learned and able to explain it to people compactly and understandably? What this means is that you’re able to think effectively. There are some standard guidelines that we can use to be able to think effectively. These standards are what logic is about.
What are the four basic elements of logic?
The first element of logic is classification, which is the way we sort concepts. Concepts are ideas that represent things we know, they could be specific, broad, real, or fake. For example, a concept could be dog, unicorn, art, animals. The idea is that concepts can be anything. The second element of logic is definitions. Definitions are the way we can find out what concepts mean. The third element of logic is propositions. A proposition is an assertion made about a few concepts. A few examples of propositions would be a car is a vehicle, my car is out of gas and most cars have four wheels. These are the four basic elements of logic, the rest is more complicated.
What is an argument?
An argument is a set of propositions in which a few propositions try to prove other propositions. The propositions that do the proving are the premises and the propositions that are being proved are the conclusions. An argument can come in many different shapes and sizes. It could have one premise and one conclusion. One conclusion could have multiple premises, one premise could have multiple conclusions, premises could have premises, premises could be dependent on each other or independent. These factors are important for knowing if an argument is valid. A valid argument doesn’t mean that the facts of the argument are correct, but solely that its structure is correct. Both of these need to be correct for an argument to be true.
How can an argument diagrammed?
Diagramming an argument helps with being able to put an argument into a simplified and compact form. There a quite a few ways to diagram an argument, some being more complicated than others. Let’s start with a simple example of how an argument can be diagrammed. In this diagramming method, a step from one proposition to another is represented by an arrow, and the propositions are represented by numbers. So a proposition with one premise and one conclusion would be represented like this:
If an argument has two dependent premises and one conclusion then it would look like this:
1 + 2
There could be multiple steps in an argument where one proposition is a conclusion of one proposition, but also the premise of another. I’ll show an example where there are three premises with three steps.
These are some examples of how this diagramming method works, it gets more complicated with things like implicit premises.
What are fallacies?
The simplest definition of a fallacy is a mistake that was made in reasoning, but a more common definition refers to common mistakes that might seem correct at first but fall apart at a closer inspection of the argument. I’ll give examples of a few fallacies and why they’re wrong. The first type of fallacies is subjectivist fallacies. They include fallacies that in one way involve bias or prejudice. The simplest form of this kind of fallacy is the fallacy of subjectivism. The fallacy goes like this: Because I think/want a to be true = a is true. This argument is false because our opinion on something is used as a premise.
The second type of fallacies are fallacies that are related to credibility. One fallacy of this type is called the Ad Hominem fallacy. The Ad Hominem fallacy consists of attacking the person who said the argument instead of the argument itself. An example of this kind of fallacy would be this: B said a and B has a negative trait = a is false. This is false because what traits somebody isn’t related to somebody’s argument whatsoever.
The third type of fallacies are fallacies of context. These types of fallacies have a logical gap in their arguments because their premises are incomplete and don’t give the full picture. One fallacy of this type is post hoc propter hoc, which is Latin for “after this, therefore because of this”. It’s usually shortened to just post hoc, however. How the fallacy works is that because something happened before something else, then that thing caused the other thing. How this works is: A occurred before B = A caused B. This is false because many things come after and before each other that have nothing to do with each other.
The fourth type of fallacies are fallacies of logical structure. These kinds of fallacies are fallacies that have subtle logical errors in them. The simplest fallacy of this type is the fallacy of begging the question, AKA a circular argument. How the fallacy works is that the conclusion of the argument is also a premise of the argument. The simplest example of this fallacy would look like this: A = A.
What is deductive logic?
Parts 3 and 4 of Art of Reasoning include Classical- and Modern deductive logic respectively. They include complex ways of diagramming arguments and assessing the validity of those arguments. The book also has a fifth part which includes inductive logic, but I haven’t read that part of the book yet. Parts 3 and 4 include syllogisms, propositional logic, and predicate logic. These are all very complicated, but I can give some general information on how these systems work. Syllogisms are steps of instructions that make it easier to determine the validity of an argument. The main difference between classical deductive- and modern deductive logic is that in the latter everything is turned into symbols. In the former, however, the forms of propositions are not turned into symbols. These forms are words like all, some, if, then, etc.
Why is logic usefull?
Being good at logic is very important because then you’re able to express your thoughts and give good arguments. This is an essential skill that nowadays very few people know. This book is an introductory book to logic, but even then logic is very complicated. Many times I’ve been completely and utterly confused by what this book is trying to teach me. In the later chapters, there is way too much information that you are trying to remember. However, if you can push through and become an expert at logic, then you will be better than almost every person on the planet.